Adrian has revealed Liverpool have been interested in his services for years.
The 32-year-old was signed on a free transfer by the Reds on Monday, after his six-year spell at West Ham United expired at the conclusion of last season.
"To be fair, there was interest years ago, but the real interest was in the last few days," Adrian told the club's website.
"We spoke every day with my agent and we had other options to move, because I finished with West Ham as a free agent last season. Finally, the last call was yesterday was to go to London to do all the stuff. Obviously I'm really happy to be here.
"It's a great step in my career right now, after six good seasons at West Ham. I got experience in the Premier League and I'm coming to a big club to fight for everything. It's a good challenge, a big challenge for me to face, challenging with big players here."
